The problem provided in the image states the following:

1(a)
Given the function $f : x \to |x + 8|$, find the possible values of $x$ when the image (output) is 3.

This means you are tasked with solving the equation $|x + 8| = 3$.

Solution

The absolute value equation $|x + 8| = 3$ implies two possible cases:

1. $x + 8 = 3$
2. $x + 8 = -3$

Case 1:
$x + 8 = 3$
$x = 3 - 8$
$x = -5$

Case 2:
$x + 8 = -3$
$x = -3 - 8$
$x = -11$

Answer:

The possible values of $x$ are $\mathbf{-5}$ and $\mathbf{-11}$.

Let me know if you would like a detailed explanation or have further questions!

Related Questions

1. What happens when the absolute value equation is equal to 0?
2. How do you graph the function $f(x) = |x + 8|$?
3. Can absolute value equations have no solution? Why or why not?
4. What are the properties of absolute value functions?
5. How can absolute value inequalities be solved systematically?

Tip

When solving $|A| = B$, always split it into the two cases $A = B$ and $A = -B$, provided $B \geq 0$.